scipy.signal.

lti#

class scipy.signal.lti(*system)[source]#

Continuous-time linear time invariant system base class.

Parameters:

*systemarguments

The lti class can be instantiated with either 2, 3 or 4 arguments. The following gives the number of arguments and the corresponding continuous-time subclass that is created:

2: TransferFunction: (numerator, denominator)

3: ZerosPolesGain: (zeros, poles, gain)

4: StateSpace: (A, B, C, D)

Each argument can be an array or a sequence.

Attributes:

dt: Return the sampling time of the system, None for lti systems.
poles: Poles of the system.
zeros: Zeros of the system.

Methods

`bode`([w, n])	Calculate Bode magnitude and phase data of a continuous-time system.
`freqresp`([w, n])	Calculate the frequency response of a continuous-time system.
`impulse`([X0, T, N])	Return the impulse response of a continuous-time system.
`output`(U, T[, X0])	Return the response of a continuous-time system to input U.
`step`([X0, T, N])	Return the step response of a continuous-time system.
`to_discrete`(dt[, method, alpha])	Return a discretized version of the current system.

See also

ZerosPolesGain, StateSpace, TransferFunction, dlti

Notes

lti instances do not exist directly. Instead, lti creates an instance of one of its subclasses: StateSpace, TransferFunction or ZerosPolesGain.

If (numerator, denominator) is passed in for *system, coefficients for both the numerator and denominator should be specified in descending exponent order (e.g., s^2 + 3s + 5 would be represented as [1, 3, 5]).

Changing the value of properties that are not directly part of the current system representation (such as the zeros of a StateSpace system) is very inefficient and may lead to numerical inaccuracies. It is better to convert to the specific system representation first. For example, call sys = sys.to_zpk() before accessing/changing the zeros, poles or gain.

Array API Standard Support

lti has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	⛔
PyTorch	⛔	⛔
JAX	⛔	⛔
Dask	⛔	n/a

See Support for the array API standard for more information.

Examples

>>> from scipy import signal

>>> signal.lti(1, 2, 3, 4)
StateSpaceContinuous(
array([[1]]),
array([[2]]),
array([[3]]),
array([[4]]),
dt: None
)

Construct the transfer function \(H(s) = \frac{5(s - 1)(s - 2)}{(s - 3)(s - 4)}\):

>>> signal.lti([1, 2], [3, 4], 5)
ZerosPolesGainContinuous(
array([1, 2]),
array([3, 4]),
5,
dt: None
)

Construct the transfer function \(H(s) = \frac{3s + 4}{1s + 2}\):

>>> signal.lti([3, 4], [1, 2])
TransferFunctionContinuous(
array([3., 4.]),
array([1., 2.]),
dt: None
)